*ABCD*and

*BFGE,*sharing a vertex. Given that

*AE*= 5, what is the length of

*DG?*My first thought was that surely the problem was … Continue Reading ››

Twitter is a great place to find geometry problems. The July 22, 2017 post of xylem presented the image below with two squares, *ABCD* and *BFGE,* sharing a vertex. Given that *AE* = 5, what is the length of *DG?*
My first thought was that surely the problem was … Continue Reading ››

Estimation is an important mathematical skill, yet we rarely ask students to make estimates that relate to fractions. As part of the Dynamic Number project, we created a "mystery" fraction challenge that presents a green point somewhere between 0 and 1 on the number line. The point's location can be represented as a fraction with … Continue Reading ››

The four Web Sketchpad activities below from our Dynamic Number project provide a sequenced collection of challenges and games that develop an area model approach to binomial multiplication and factoring. You can click any of the images to open the interactive websketches on a separate page.
**Dynamic Algebra Tiles, Part One**

In the first websketch, students … Continue Reading ››

I've lost track of how many parents have quizzed me as to why the mathematics their children are learning is so different from what they remember in school. "Why must my kids study more than one way to multiply? Isn't memorizing their multiplication facts enough?" is a frequent lament. James Tanton, Mathematician in Residence at the … Continue Reading ››

In my previous post, I wrote about cross number puzzles—puzzles that mix arithmetic and logic to introduce students to place value, commutativity, and the addition and subtraction algorithms.
Now, I'd like to present a variant of cross number puzzles that adds some algebra to the mix. Below (and here on its own page) are … Continue Reading ››

We live in a golden age of number puzzles. Sudoku is probably the most famous of all modern-day number puzzles, but there are many Japanese puzzles that are also gaining popularity, such as KenKen and Menseki Meiro. In this post, I'd like to introduce a number puzzle for young learners that predates … Continue Reading ››

What would it take to build a better number grid for young learners? A typical number grid contains 10 columns with the numbers progressing from 1-10, 11-20, 21-30 and so on, from row to row. We decided to upend this tradition and make a dynamic number grid with Web Sketchpad that allows students to choose … Continue Reading ››

In the interactive websketch below (and here on its own page), *ABCD* is an arbitrary quadrilateral whose midpoints form quadrilateral *EFGH*. Drag any vertex of *ABCD*. What do you notice about *EFGH*?
The midpoint quadrilateral theorem, attributed to the French mathematician Pierre Varignon, is relatively new in the canon of geometry theorems, dating to 1731. Mathematics educator Chris Pritchard … Continue Reading ››

In my last post, I presented a lovely geometry problem from Japan that was ideally suited to a dynamic geometry approach. Below is a new problem whose construction is nearly identical to the original one. The text says, "Five isosceles triangles have their bases on one line, and there are 10 rhombi. One length of the rhombus … Continue Reading ››

Here is a wonderful geometry problem from Japan: The five triangles below are all isosceles. The quadrilaterals are all rhombi. The shaded quadrilateral is a square. What is the area of the square?
I wondered at first whether the English translation of the problem was correct because with so many side … Continue Reading ››